A hallmark of most physical systems is spatial locality.
Points close to one another will usually have a
stronger coupling than points that are far from one another.
For example, basic physical processes such as convection and diffusion are spatially local.
In most DMD applications, the data are collected from a spatial grid, but the grid rarely plays a role in the DMD analysis beyond forming the energy norm [1]}.
In fact, the output of the exact DMD algorithm remains invariant to unitary transformations on the rows and columns of the data matrices, so that randomly shuffling the rows (i.e., the spatial locations) will result in identical DMD models with the corresponding shuffling of the rows of the modes [2]}, [3]}.
Knowledge of the underlying grid from which the data were collected
enables us to bias the learning
process to prioritise relationships that we expect to have a strong local coupling.
